A decision-making framework based on the Fermatean hesitant fuzzy distance measure and TOPSIS

A particularly useful assessment tool for evaluating uncertainty and dealing with fuzziness is the Fermatean fuzzy set (FFS), which expands the membership and non-membership degree requirements. Distance measurement has been extensively employed in several fields as an essential approach that may successfully disclose the differences between fuzzy sets. In this article, we discuss various novel distance measures in Fermatean hesitant fuzzy environments as research on distance measures for FFS is in its early stages. These new distance measures include weighted distance measures and ordered weighted distance measures. This justification serves as the foundation for the construction of the generalized Fermatean hesitation fuzzy hybrid weighted distance (DGFHFHWD) scale, as well as the discussion of its weight determination mechanism, associated attributes and special forms. Subsequently, we present a new decision-making approach based on DGFHFHWD and TOPSIS, where the weights are processed by exponential entropy and normal distribution weighting, for the multi-attribute decision-making (MADM) issue with unknown attribute weights. Finally, a numerical example of choosing a logistics transfer station and a comparative study with other approaches based on current operators and FFS distance measurements are used to demonstrate the viability and logic of the suggested method. The findings illustrate the ability of the suggested MADM technique to completely present the decision data, enhance the accuracy of decision outcomes and prevent information loss

A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making

The aim of this paper is to provide a methodology to hesitant fuzzy multiple attribute decision making using technique for order preference by similarity to ideal solution (TOPSIS) and distance measures. Firstly, the inadequacies of the existing hesitant fuzzy TOPSIS method are analyzed in detail. Then, based on the developed hesitant fuzzy ordered weighted averaging weighted aver-aging distance (HFOWAWAD) measure, a modified hesitant fuzzy TOPSIS, called HFOWAWAD-TOPSIS is introduced for hesitant fuzzy multiple attribute decision making problems. Moreover, the advantages and some special cases of the HFOWAWAD-TOPSIS are presented. Finally, a numerical example about energy policy selection is provided to illustrate the practicality and feasibility of the developed approach

Distance Measures for Reduced Ordering Based Vector Filters

Reduced ordering based vector filters have proved successful in removing long-tailed noise from color images while preserving edges and fine image details. These filters commonly utilize variants of the Minkowski distance to order the color vectors with the aim of distinguishing between noisy and noise-free vectors. In this paper, we review various alternative distance measures and evaluate their performance on a large and diverse set of images using several effectiveness and efficiency criteria. The results demonstrate that there are in fact strong alternatives to the popular Minkowski metrics

A general unified framework for pairwise comparison matrices in multicriterial methods

In a Multicriteria Decision Making context, a pairwise comparison matrix $A=(a_{ij})$ is a helpful tool to determine the weighted ranking on a set $X$ of alternatives or criteria. The entry $a_{ij}$ of the matrix can assume different meanings: $a_{ij}$ can be a preference ratio (multiplicative case) or a preference difference (additive case) or $a_{ij}$ belongs to $[0,1]$ and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). For the multiplicative case, a consistency index for the matrix $A$ has been provided by T.L. Saaty in terms of maximum eigenvalue. We consider pairwise comparison matrices over an abelian linearly ordered group and, in this way, we provide a general framework including the mentioned cases. By introducing a more general notion of metric, we provide a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix

Optimal Siting of Electric Vehicle Charging Stations Using Pythagorean Fuzzy VIKOR Approach

Site selection for electric vehicle charging stations (EVCSs) is the process of determining the most suitable location among alternatives for the construction of charging facilities for electric vehicles. It can be regarded as a complex multicriteria decision-making (MCDM) problem requiring consideration of multiple conflicting criteria. In the real world, it is often hard or impossible for decision makers to estimate their preferences with exact numerical values. Therefore, Pythagorean fuzzy set theory has been frequently used to handle imprecise data and vague expressions in practical decision-making problems. In this paper, a Pythagorean fuzzy VIKOR (PF-VIKOR) approach is developed for solving the EVCS site selection problems, in which the evaluations of alternatives are given as linguistic terms characterized by Pythagorean fuzzy values (PFVs). Particularly, the generalized Pythagorean fuzzy ordered weighted standardized distance (GPFOWSD) operator is proposed to calculate the utility and regret measures for ranking alternative sites. Finally, a practical example in Shanghai, China, is included to demonstrate the proposed EVCS sitting model, and the advantages are highlighted by comparing the results with other relevant methods.Peer Reviewe